Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Can you use the information to find out which cards I have used?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you substitute numbers for the letters in these sums?
Can you find all the different ways of lining up these Cuisenaire
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you use this information to work out Charlie's house number?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Ben has five coins in his pocket. How much money might he have?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This dice train has been made using specific rules. How many different trains can you make?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
This task follows on from Build it Up and takes the ideas into three dimensions!
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Can you find all the ways to get 15 at the top of this triangle of numbers?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?